2006/08/31 by Christine Bachoc, Frank Vallentin · 4 citations
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Machine Learning and Algorithms #graph theory and CDMA systems #math.CO #math.MG #msc:52C17 #msc:90C22
paper · pdf · doi:10.1090/s0894-0347-07-00589-9
published as J. Amer. Math. Soc. 21 (2008), 909-924 · 17 pages, (v4) references updated, accepted in Journal of the American Mathematical Society
arxiv created 2007/10/03 · openalex publication_date 2007/11/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Recently A. Schrijver derived new upper bounds for binary codes using semidefinite programming. In this paper we adapt this approach to codes on the unit sphere and we compute new upper bounds for the kissing number in several dimensions. In particular our computations give the (known) values for the cases <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n equals 3 comma 4 comma 8 comma 24"> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mn>4</mml:mn> <mml:mo>,</mml:mo> <mml:mn>8</mml:mn> <mml:mo>,</mml:mo> <mml:mn>24</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">n = 3, 4, 8, 24</mml:annotation> </mml:semantics> </mml:math> </inline-formula> .